1. Field of the Invention
The present invention relates to a resonant cavity. More particularly, the present invention relates to a resonant cavity using a photonic crystal.
2. Description of the Related Art
A photonic crystal may have a structure as small as a few micrometers to as large as a few hundred micrometers. A photonic crystal is an optical device formed in a regular, periodic arrangement of substances having different refractive indices or dielectric constants, which can form a complete band gap for preventing a specific polarization of waves from propagating therethrough as well as an absolute band gap for preventing light from propagating therethrough regardless of the polarization of the light. Accordingly, a photonic crystal is suitable for use in optic-related devices, such as filters, light waveguides, optic delay devices, lasers, and the like.
In general, photonic crystals may have three types of structures, such as one-dimensional, two-dimensional, and three-dimensional, depending on the number of directions of periodic structure. For such a photonic crystal, a variety of concrete shapes in each dimension has been proposed. For example, in a case of a two-dimensional photonic crystal, the crystal is characterized by a lattice shape, lattice constant, inserted rod shape, and so on. Further, when a circular rod is inserted, a complete band gap can be achieved that prevents light having a wavelength of approximately twice as long as a lattice constant from propagating in any direction in a periodic structure with proper selections of a radius thereof, a dielectric permittivity, and other similar characteristics.
FIG. 1 illustrates an elevated view of a conventional photonic crystal-based cavity. A cavity 10 has a periodic arrangement of air holes 14 and a local defect 16 disrupting the periodic arrangement in a dielectric slab 12 having a predetermined dielectric permittivity.
Here, the local defect 16 spatially confines electromagnetic fields and generates an electromagnetic mode in a band gap. Further, electromagnetic radiation in a direction vertical to a two-dimensional plane is confined by total internal reflection (TIR).
Accordingly, light incident through a structure having an ordered air hole arrangement 14 and a local defect 16 in the dielectric slab 12 can be captured on a portion of the local defect 16, through which it can be used as a cavity for a laser having a very high quality factor Q.
FIG. 2 illustrates a plan view of a structure of a conventional photonic crystal having a plurality of band gaps. Inserted in the structure of a photonic crystal having a plurality of band gaps are a plurality of second dielectric substances 25 having a second dielectric permittivity, the second dielectric substances 25 being arranged in a first periodic structure with respect to at least one or more directions on the plane formed by a first dielectric substance 21, e.g., a slab, having a first dielectric permittivity, and a plurality of third dielectric substances 25′ having a third dielectric permittivity, the plurality of third dielectric substances 25′ being arranged in a second periodic structure in a unit cell formed by the plurality of second dielectric substances 25. The plurality of second dielectric substances 25 and the plurality of third dielectric substances 25′ are arranged to have a third periodic structure with respect to at least one or more directions.
Here, the plurality of third dielectric substances 25′ can be used with the dielectric permittivity changing while the size thereof is maintained, or, can be used with the size varying while the dielectric permittivity is maintained. Further, the plurality of third dielectric substances 25′ can be used while the size and the dielectric permittivity both vary at the same time.
FIG. 3 is a graph showing respective frequency gaps appearing when the magnitude of a radius of the third dielectric substance 25′ varies. In this case, the photonic crystal includes the plurality of second dielectric substances 25 having a dielectric permittivity of 8.9, a radius R and a lattice constant “a” that are disposed in the first dielectric slab 21 having a dielectric permittivity ∈a and the plurality of third dielectric substances 25′ having a radius R′ that are inserted in the central portions of the unit cells of the lattice structure of the plurality of second dielectric substances 25. The radius R′ of the third dielectric substance take a value of             0.2      ⁢      α              5      ⁢              2              ,            0.4      ⁢      α              5      ⁢              2              ,            0.6      ⁢      α              5      ⁢              2              ,            0.8      ⁢      α              5      ⁢              2              ,      and    ⁢                  ⁢                  0.2        ⁢        α                    2            which come from five equal divisions of a distance from   0  ⁢          ⁢  to  ⁢          ⁢                    0.2        ⁢        α                    2              .  Meanwhile, in order for the final photonic crystal structure resulting from the insertion of the plurality of third dielectric substances 25′ to become a scale version of √{square root over (2)} times, the radius R of the plurality of second dielectric substances 25 should be changed to have the five equal divisions between       0.2    ⁢    a    ⁢                  ⁢    and    ⁢                  ⁢                  0.2        ⁢        a                    2              ,as the radius R′ of the third dielectric substances 25′ changes. When the direction of insertions are from left to right in FIG. 3, reference numeral 35′, seen from the left, denotes a lower frequency value of a first band gap in the initial photonic crystal, and reference numeral 36′ denotes an upper frequency value of the first band gap. Reference numeral 31′ denotes a frequency at one insertion position where a band gap occurs during the insertions, reference numeral 31, seen from the right, denotes a lower frequency value of the first band gap in a finally inserted photonic crystal, and reference numeral 32 denotes an upper frequency value of the first band gap. Further, reference numeral 35 is a frequency value at one insertion position at which the band gap disappears.
Through interpolating periodic configuration and sizes of different dielectric substances as above, one is able to make a photonic crystal having a plurality of band gaps at desired positions.
Although the conventional photonic crystal structure is able to have a plurality of band gaps through the respective insertion of dielectric substances, it is not suitable for use as a cavity. Further, since a cavity using the conventional photonic crystal has a single band gap, it causes a problem in that a resonant mode can be formed only for a single wavelength of a single band.